A353878 Number of tilings of a 3 X n rectangle using right trominoes, dominoes and 1 X 1 tiles.

1, 3, 44, 369, 3633, 34002, 323293, 3058623, 28982628, 274494621, 2600148629, 24628666626, 233286962601, 2209723174731, 20930806288252, 198259418947833, 1877940242218857, 17788105074906162, 168491350295593637, 1595972975308532199, 15117273008425964916

Offset: 0

Author

Gerhard Kirchner, May 09 2022

Keywords

• nonn
• easy

Comments

Tiling algorithm see A351322.

Examples

			a(2)=44
The number of tilings (mirroring included) using r trominoes
      ___   ___        ___
r=1: |  _| | |_| r=2: |  _| r=0: 22 = A030186(3)
     |_|3| |___|      |_| |
     |___| |_2_|      |___|
      4*3 + 4*2   +    2*1   +   22 = 44
Legend:
   ___              ___      ___
  |_2_| stands for |___| or |_|_|
     _                _        _        _
   _|3|             _| |     _|_|     _|_|
  |___| stands for |_|_| or |___| or |_|_|
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,33,3,-40,15).

Crossrefs

Cf. A030186, A127867, A165716, A351322, A352589, A353877, A353879.

Programs

Maxima

See A352589.

Formula

G.f.: (1-3*x-7*x^2+3*x^3-2*x^4) / (1-6*x-33*x^2-3*x^3+40*x^4-15*x^5).

a(n) = 6*a(n-1) + 33*a(n-2) + 3*a(n-3) - 40*a(n-4) + 15*a(n-5).